A Generalization of σ-Permutability

作     者：Zhigang Wang Jin Guo Inna N.Safonova Alexander N.Skiba 

作者机构：School of ScienceHainan UniversityHaikou 570228HainanPeople’s Republic of China Department of Applied Mathematics and Computer ScienceBelarusian State University220030 MinskBelarus Department of Mathematics and Technologies of ProgrammingFrancisk Skorina Gomel State University246019 GomelBelarus 

出 版 物：《Communications in Mathematics and Statistics》 (数学与统计通讯（英文）)

年 卷 期：2022年第10卷第3期

页      面：565-579页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by the NNSF of China(No.12171126,11961017) supported by Ministry of Education of the Republic of Belarus(grant 20211328) supported by the BRFFR(grant F20R-291) 

主　　题：Finite group σ-nilpotent group П-semiprojector П-covering subgroup system σ-subnormal subgroup 

摘      要：Throughout this paper,all groups are finite and G always denotes a finite group;σis some partition of the set of all primes P.A group G is said to beσ-primary if G is aπ-group for someπ∈σ.Aπ-semiprojector of G[29]is a subgroup H of G such that HN/N is a maximalπ-subgroup of G/N for all normal subgroups N of ***П⊆σ.Then we say thatχ={X_(1),...,X_(t)}is aП-covering subgroup system for a subgroup H in G if all members of the setχareσ-primary subgroups of G and for eachπ∈Пwithπ∩π(H)≠φthere are an index i and aπ-semiprojector U of H such that U≤X_(i).We study the embedding properties of subgroups H of G under the hypothesis that G has aП-covering subgroup systemχsuch that H permutes with X^(x)for all X∈χand x∈*** well-known results are generalized.